Shap3d47.dat, 47th 'shape' file for CPO3D

Square hole in a sphere, by users equation.

For information on the option for users equations, see users equations.

Developed from shap3d39, square hole in circular disc..

The sphere has a radius of R, and so z = sqrt(R^2 - x^2 - y^2), always.

The equations, say g1(x,y,z), for the inner square edge are

x = s, y = s*tan(phi), where phi = 0 to pi/4.

The equations, say g2(x,y,z), for the outer circular edge are

x = r*cos(phi), y = r*sin(phi).

In the usual fashion we can combine these by using the general equation

g(x,y,z) = (1 - f)*g1 + f*g2,

where f goes from 0 to 1.

This reproduces g1 when f = 0, and g2 when f = 1.

Here s = 0.25, r = 0.75, R = 1 and 3 symmetry planes are used.

The equation for z looks complicated, but is essentially sqrt(R^2 - x^2 - y^2).

The '+1.e10' avoids sqrt(0).

Simulting a rectangular slot in a sphere is clearly possible, but more compicated.

The data, as they appear in the data file, are:

f 0 1 name of variable number 1 and its limits

phi 0 0.785398 name of variable number 2 and its limits

r 0.75 name of parameter number 1 and its fixed value

s 0.25 name of parameter number 2 and its fixed value

R 1 name of parameter number 3 and its fixed value

0 name of parameter number 4 and its fixed value

s*(1-f)+r*cos(phi)*f

s*tan(phi)*(1-f)+r*sin(phi)*f

sqrt(R^2-((s*(1-f)+r*cos(phi)*f)^2+(s*tan(phi)*(1-f)+r*sin(phi)*f)^2)+1.e-8)

1 1 numbers of 2 applied voltages (can be same)

6 8 numbers of subdivisions of variables 1 and 2

(The program has corrected the less accurate value that was entered for pi/4.)